AIBU to ask my lodger to cut down on washing machine use?

What the hell? Who could get by on 2 washes per week? Also, OP absolutely cannot specify what those washes must be.

It's her house and she damn well can police how often the lodger does laundry.
I would say something like this;
"Hey [Lodger], do you have a quick second? I noticed the other day you ran the washer and dryer for just a couple of items. I'm really trying to keep our household footprint down—both for the environment and because utility bills are so high right now. Because of that, from now on, I need to make it a firm rule that we only run the machines for full loads. Otherwise it wastes a huge amount of water and energy. If you ever just need one or two things washed quickly, you'll need to hand-wash them or wait until you have a full basket. Thanks, I really appreciate you taking this onboard."

I wash when it's enough for a load. Never separate anything, don't understand why you'd need to. Don't understand the 'towels must be washed alone' thing either. Although my over 15 year old hotpoint packed up last week so am on my 5th load today including a bedding wash cos it was minging.
Also my new machine has a 4 hour eco wash but also a 15 min quick wash.

Just charge him more?

Sixty years ago our buildings were pitch black, filthy with soot and the air quality in the city would turn the inside of your nose black.

I was not talking about global trade or mass consumerism. I was talking about washing your clothes - which is an absolute necessity.

A full load can be difficult for a single person, especially due to having to separate whites, colours, delicates etc.

But half a load is the minimum, imo…

I had this very issue with a previous lodger. Turns out he only possessed two pairs of boxers, two T shirts and two pairs of trousers. He did it differently in the sense that he would do a full load, but would wash nearly every day and would put my washing in each time he had to wash something of his.

The washing machine being on every single day drove me nuts, but I didn't like the thought of him dealing with my 'smalls' either!

So true.

Climate change has everything to do with excessive energy use and consumerism. 60 years ago, the family laundry once done once a week usually on a Monday for some reason , and many people only had one trip on a plane each year ,if that. Goods were not shipped halfway round the world either, and many goods were usually built to last longer.
It seems there is a sense of entitlement nowadays to exploit resources just because some people have the money so do so ,without even considering the consequences for the next generation. It can't really be energy efficient to put one pair of gym shorts as a single load in a washing machine. I t might only cost £.0.30p in money to wash those shorts, , but the long term cost is much greater than just cash.

Yes, people not overloading the machine and washing their work uniforms is driving climate change and it has nothing to do with all the private jet users and mega factories in China and India.

I genuinely don’t understand how couples can do one or two loads of washing a week. I’m single, not particularly precious and a bit of a slob and I can easily do 4-5 loads. And I always fill the machine.

Washing machines are not expensive to run. They’re even cheaper on an eco wash. A long wash is good for the health of the machine.

You don’t know why he was washing only one item and he might have good reason - if he had stained or soiled the shorts in some way he might have had to wash it alone.

Ultimately you’ve made the decision to take in a lodger and this means you need to accept some compromises. I think this is a very small concession for you to make in context and if this is the worst thing he does I would be thanking my lucky stars.

If your bills are higher than expected, tell him you’re putting the rent up by a few quid.

Well, yes, because I don't want to end up with grey whites or shrunken delicates (voice of experience).

I’m shocked that this fella would do this. It’s mad! Honestly they need to bring back home economics or something at school as if someone has grown up thinking that such wasteful behaviour is ok my god. First lesson of environmental good practice is reduce consumption. I would have to say something (as nicely as I could). (I take water use very seriously- I’m on a private water supply and if you’ve ever had that fail, you know how precious it is.

I’d just say it’s not ok to use washing machine for less than half a load. My machine had a quick 1 hour setting for 4kg. I usually use that for half a load rather than the 3 hour range 10kg cycle.

I wonder if you would do the same number of loads if you had to use a launderette though?

Some people seem to do lot of loads per week for a single adult. OP mentioned a her lodger doing a single pair of gym shorts . Are fewer people waiting until they have enough laundry of a particular type to do full loads? No wonder climate change is on the increase with this level of energy use, if some people are only putting a couple of items at a time in the machine..

I don’t know about anybody else, but I find one bath sheet a week quite enough, as long as there’s somewhere to dry it properly in between uses.

And I often put white clothes in with my (white) towels.

That wouldn't work for me as I do washes of different temperatures too. I generally do a whites, a gentle 30-degree wash, a 40-degree for underwear and gym stuff and another 40-degree or sometimes hotter for bedding/towels.
I'm sure I'm not the only one.

Ask him to limit him to limit to three loads per week - lights, darks, bedding.

My family of 6 does 5 loads a week and that includes all the bedding at weekends!!!

Presumably people who say stuff like this have a 12kg washing machine. Mine is only 7kg so I can't just throw everything in in one go. I've got three fleece blankets, a single fitted sheet and a baby towel in my washing machine and it sounded a bit iffy on the spin cycle just now!

It's because they get so heavy with water. I don't wash mine in the washing machine, I stick it in a bucket with very hot water and washing powder and leave it to soak, then rinse it with the shower, wring it out and hang it up outside. If you wash it with other bath mats or towels it should spin. My bath mats are hair magnets so I don't like putting them in the washing machine.

Could you just tell him he can do two loads a week. Anything extra you will charge for. When my exdh was a lodger when he was young his landlady didn’t allow him to use the washing machine. He went to the launderette. Keep in mind this is your house and your lodger rents one room with, I’m assuming, reasonable use of bathroom, kitchen. If he started taking three baths a day I’m sure you’d act quickly. What he’s doing sounds unreasonable to me. I’ve shared my home with students, adults and looked after children so have experienced most scenarios

Do you mean when do I run it so it doesn't annoy me? The machine lives in a cupboard and I shut the door. I work upstairs, so I can hear it, but only quietly.
Or do you mean so I can hang stuff afterwards? Because I work at home I can put it on and stop work briefly to hang things whenever I need to. In good drying weather I do try to put it on early so I can get it out into the garden for maximum sun.

Especially if his rent includes electricity, she can say something! Even if the contract doesn't specify 'reasonable use', that can surely be implicit.